Spurred by the enormous data processing demands of the Human Genome Project, genetics is quickly becoming a computational science. This proposal addresses some of the computational issues arising in human gene mapping. Family studies, sperm typing, and radiation hybrids all present unique modeling computational challenges in constructing high-resolution gene maps. Even with ultra-fast computers, good algorithm design and software development are imperative. The theory of hidden Markov chains provides a common framework for likelihood evaluation in these three gene-mapping strategies. When combined with the EM algorithm for maximum likelihood evaluation, fast estimation procedures are possible. The same advantages may well accrue in the reconstruction of evolutionary trees. Because estimation must be carried out for a particular order of the loci to be mapped, there is also the added complexity of investigating a large number of candidate orders. Better Bayesian and heuristic techniques for identifying the best order need to be developed. Finally, better stochastic models of genetic recombination are obviously important in both family studies and sperm typing. Allele lumping and Monte Carlo Markov chains are other pertinent computational devices. Allele lumping done on a local basis within a pedigree may eliminate some the major computational bottlenecks in linkage calculations. Our ongoing work on the Metropolis algorithm in pedigree analysis and on exchange algorithms for testing independence in high- dimensional contingency tables also demonstrates some of the great promise simulation methods hold for genetics. Further development of these simulation tools is warranted by applications as diverse as affecteds-only methods of linkage analysis, identification of the most probable genotype vector in a pedigree, and testing for Hardy-Weinberg and linkage equilibrium in multilocus population data. This proposal suggests several ambitious avenues for research in the above areas. Our intention is to pursue the most promising of these leads while keeping an opportunistic eye on new developments in genetics for additional problems. Production of usable software will be a natural outgrowth of our investigations.